U.S. patent number 5,280,425 [Application Number 07/558,970] was granted by the patent office on 1994-01-18 for apparatus and method for production planning.
This patent grant is currently assigned to Texas Instruments Incorporated. Invention is credited to John C. Hogge.
United States Patent |
5,280,425 |
Hogge |
January 18, 1994 |
Apparatus and method for production planning
Abstract
Apparatus and method for production planning in a manufacturing
facility is provided. The apparatus and method generates a
plurality of theoretical plans and a constraint-based model for
receiving one of the theoretical production plans, and applying at
least one constraint thereto. Further, a cost function is computed
for the theoretical production plans. Then, the apparatus and
method searches for a feasible production plan among the plurality
of theoretical plans, where the feasible plan is the plan which
does not violate the applied constraint and has the least computed
cost function.
Inventors: |
Hogge; John C. (Richardson,
TX) |
Assignee: |
Texas Instruments Incorporated
(Dallas, TX)
|
Family
ID: |
24231749 |
Appl.
No.: |
07/558,970 |
Filed: |
July 26, 1990 |
Current U.S.
Class: |
712/300;
700/97 |
Current CPC
Class: |
G06Q
10/06 (20130101); Y02P 90/02 (20151101); Y02P
90/20 (20151101) |
Current International
Class: |
G06Q
10/00 (20060101); G06F 015/20 () |
Field of
Search: |
;364/401-406,468,2MSFile |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Driscoll and Emmons, "Scheduling Production on One Machine with
Changeover Costs", AIIE Transactions, vol. 9, No. 4, Dec. 1977, p.
388. .
Glassey "Minimum Change-Over Scheduling of Several Products on One
Machine", Options Research, col. 16, No. 2, Mar.-Apr. 1968. .
Lasdon and Terjung "An Efficient Algorithm for Multi-Item
Scheduling", Options Research, vol. 19, p. 946. .
Leachman, Preliminary Design and Development of a Corporate-Level
Production Planning System for the Semiconductor Industry,
Operations Research Center, U-California, Berkeley, May 18, 1987.
.
Saad, "An Overview of Production Planning Models: Structural
Classification and Empirical Assessment", Int. J. Prod. Res., 1982,
vol. 20, No. 1, p. 105..
|
Primary Examiner: Envall, Jr.; Roy N.
Assistant Examiner: Poinvil; Frantzy
Attorney, Agent or Firm: Troike; Robert L. Heiting; Leo N.
Donaldson; Richard L.
Claims
What is claimed is:
1. Apparatus for production planning in a manufacturing facility,
comprising:
means for generating a plurality of theoretical plans;
a constraint-based model for receiving one of said theoretical
production plans, and applying at least one constraint thereto;
means for computing a cost function per addition to work in
response to said theoretical production plan; and
heuristic means for searching for a feasible production plan among
said plurality of theoretical plans, said feasible plan within said
applied constraint and having the least computed cost function
value per addition to work.
2. The apparatus, as set forth in claim 1, wherein said
constraint-based model applies a plurality of constraints to each
of said theoretical production plan, and said feasible plan is
within said plurality of constraints.
3. The apparatus, as set forth in claim 1, wherein said
constraint-based model comprises means for applying a production
capacity constraint of said manufacturing facility to said
theoretical plan, said manufacturing facility having at least one
machine and wherein said capacity constraint applying means further
includes:
means for storing and providing an availability of each
machine;
means for controlling an amount of work-in-process;
means for storing and providing a number of work hours of said
manufacturing facility; and
means for receiving said machine availability, work-in-process and
work hours and computing the maximum amount of usage of said
machine.
4. The apparatus, as set forth in claim 3, wherein said capacity
constraint applying means includes:
means for storing and providing an amount of usage per machine;
and
means for receiving said machine usage and computing an amount of
current usage per machine in response thereto.
5. The apparatus, as set forth in claim 4, said capacity constraint
applying means further comprises means for formulating said
production capacity of said manufacturing facility in response to
said maximum usage per machine and said current usage per
machine.
6. The apparatus, as set forth in claim 1, wherein said
constraint-based model comprises means for applying a constraint
describing the amount of surplus that is feasibly produced by said
manufacturing facility.
7. The apparatus, as set forth in claim 6, said manufacturing
facility producing at least one type of product, and wherein said
surplus feasibility constraint applying means further
comprises:
means for computing expected surplus per product type in response
to said theoretical production plan; and
means for formulating said surplus feasibility constraint in
response to said computed expected surplus.
8. The apparatus, as set forth in claim 1, wherein said
manufacturing facility manufactures in units of a fixed number and
also in partial units of a number less than said fixed number,
wherein said constraint-based model comprises means for applying a
constraint describing the number of partial production units that
may be feasibly initiated by said manufacturing facility.
9. The apparatus, as set forth in claim 8, wherein said partial
unit feasibility constraint applying means comprises:
means for computing the number of units that are required in
response to said theoretical production plan;
means for computing the number of partial units that are required
in response to said theoretical production plan; and
means for formulating said partial unit feasibility constraint in
response to said computed number of units and partial units
required for said theoretical production plan.
10. The apparatus, as set forth in claim 1, said manufacturing
facility producing at least one type of product, and wherein said
cost function computing means comprises:
means for computing an expected yield per product type;
means for receiving customer demand;
means for computing a push cost per product type in response to
said computed expected yield and said received customer demand;
means for computing a pull cost per product type in response to
said computed expected yield and said received customer demand;
and
means for computing a cost function of said production plan in
response to said computed push and pull costs.
11. The apparatus, as set forth in claim 2, wherein said
theoretical production plan generating means comprises:
means for modifying a theoretical plan and generating a plurality
of children theoretical plans;
constructing a tree having said theoretical production plan as a
root node and said plurality of children theoretical production
plans as leaf nodes.
12. The apparatus, as set forth in claim 11, wherein said heuristic
searching means further comprises:
means for discarding any leaf node containing a children
theoretical production plan which contradicts said plurality of
applied constraints;
means for selecting from among remaining leaf nodes a theoretical
production plan which incurs the least cost; and
means for providing a solution production plan all of whose
children production plans contradict said applied constraint.
13. Apparatus for production planning in a manufacturing facility,
said facility manufactures quantities of at least one type of
product to meet customer demand, said apparatus comprising:
means for determining a production plan including the quantities
and types of product;
means for computing the capacity of said factory in order to
produce said determined quantities and types of product;
means for computing the maximum factory capacity;
means for comparing said computed production capacity with said
maximum factory capacity;
means for computing the cost of producing said determined
quantities and types of product per addition to work in response to
said computed production capacity being less than or equal to said
maximum factory capacity; and
means for selecting a production plan that incurs the least cost
per addition to work.
14. The apparatus, as set forth in claim 13, further comprising
means for receiving the quantities and types of product demanded by
customers.
15. The apparatus, as set forth in claim 14, further comprising
means for computing a surplus feasibility constraint that describes
the quantities and types of product which are expected to yield
large surpluses when compared to said customer demand.
16. The apparatus, as set forth in claim 15, wherein said cost
computing means computes said production cost in response to said
determined quantities and types of product generating smaller
surpluses as compared with said surplus feasibility constraint.
17. The apparatus, as set forth in claim 13, wherein said capacity
computing means further comprises:
means for modeling the machine capacity in said manufacturing
facility; and
means for computing machine usage required for said quantities and
types of product using said machine capacity model.
18. The apparatus, as set forth in claim 17, wherein said capacity
computing means further comprises:
means for storing and supplying machine availability data;
means for storing and supplying the number of work hours of said
manufacturing facility;
means for computing the work-in-process workload; and
means for computing the maximum usage per machine in response to
said machine availability data, number of work hours and
work-in-process workload.
19. The apparatus, as set forth in claim 13, wherein said cost
computing means further comprises means for computing the push cost
incurred by not producing enough quantities to meet the customer
demand.
20. The apparatus, as set forth in claim 19, wherein said cost
computing means further comprises means for computing the pull cost
incurred by producing ahead of scheduled delivery time.
21. The apparatus, as set forth in claim 20, wherein said cost
computing means further comprises means for summing said push and
pull cost to determine a total plan cost.
22. The apparatus, as set forth in claim 13, wherein said
manufacturing facility produces units of a predetermined quantity
of product and partial units of another predetermined quantity of
product and said apparatus further comprising:
means for computing the number of units of each product to be
produced;
means for computing the number of partial units of each product to
be produced;
means for determining the feasibility of producing said computed
number of units and partial units; and
said cost computing means computing said cost in response to
producing said computed number of units and partial units being
feasible.
23. A computer-implemented method for production planning in a
manufacturing facility, comprising the steps of:
generating a plurality of theoretical plans;
receiving one of said theoretical production plans, formulating a
plurality of constraints in response to said received theoretical
plan and applying said formulated constraint thereto;
computing a cost function divided by the addition to work in
response to said theoretical production plan; and
searching for a feasible production plan among said plurality of
theoretical plans, said feasible plan within said applied
constraint and having the least computed cost function value per
addition to work, wherein said searching utilizes a heuristic
search method.
24. The method, as set forth in claim 23, wherein said constraint
formulating and applying step comprises the step of formulating and
applying a production capacity constraint of said manufacturing
facility to said theoretical plan, said manufacturing facility
having at least one machine and wherein said capacity constraint
formulating step further comprises the steps of:
storing and providing an availability of each machine;
controlling a work-in-process work load;
storing and providing a number of work hours of said manufacturing
facility; and
receiving said machine availability, work-in-process and work hours
and computing the maximum amount of usage of said machine.
25. The method, as set forth in claim 24, wherein said capacity
constraint formulating step comprises the steps of:
storing and providing an amount of usage per machine; and
receiving said machine usage and computing an amount of current
usage per machine in response thereto.
26. The method, as set forth in claim 25, said capacity constraint
formulating step further comprises the step of formulating said
production capacity of said manufacturing facility in response to
said maximum usage per machine and said current usage per
machine.
27. The method, as set forth in claim 23, wherein said constraint
formulating and applying step comprises the step of formulating and
applying a constraint describing the amount of surplus that is
feasibly produced by said manufacturing facility.
28. The method, as set forth in claim 27, said manufacturing
facility producing at least one type of product, and wherein said
surplus feasibility constraint formulating step further
comprises:
computing expected surplus per product type in response to said
theoretical production plan; and
formulating said surplus feasibility constraint in response to said
computed expected surplus.
29. The method, as set forth in claim 23, wherein said
manufacturing facility manufactures in units of a fixed number and
also in partial units of a number less than said fixed number,
wherein said constraint formulating and applying step comprises the
step of formulating and applying a constraint describing the number
of partial production units that may be feasibly initiated by said
manufacturing facility.
30. The method, as set forth in claim 29, said partial unit
feasibility constraint formulating step comprises the steps of:
computing the number of units that are required in response to said
theoretical production plan;
computing the number of partial units that are required in response
to said theoretical production plan; and
formulating said partial unit feasibility constraint in response to
said computed number of units and partial units required for said
theoretical production plan.
31. The method, as set forth in claim 23, said manufacturing
facility producing at least one type of product, and wherein said
cost function computing step comprises the steps of:
computing an expected yield per product type;
receiving customer demand;
computing a push cost per product type in response to said computed
expected yield and said received customer demand;
computing a pull cost per product type in response to said computed
expected yield and said received customer demand; and
computing a cost function of said production plan in response to
said computed push and pull costs.
32. The method, as set forth in claim 23, wherein said theoretical
production plan generating step comprises the steps of:
modifying a theoretical production plan and generating a plurality
of children theoretical production plans;
constructing a tree having said theoretical production plan as a
root node and said plurality of children theoretical production
plans as leaf nodes.
33. The method, as set forth in claim 23, wherein said searching
step further comprises the steps of:
discarding any leaf node containing a children theoretical
production plan which contradicts said plurality of applied
constraints;
selecting from among remaining leaf nodes a theoretical production
plan which has the least computed cost function value; and
modifying said selected production plan to generate another
plurality of children theoretical production plans;
repeating said above steps until all children production plans from
a selected production plan contradict said plurality of
constraints; and
providing said last selected production plan as a solution
production plan.
34. A computer-implemented method for generating a production plan
for a manufacturing facility, comprising the steps of:
initializing said production plan;
generating a plurality of proposals to modify said production
plan;
formulating at least one constraint;
applying said constraints to said production plan as modified by
each of said plurality of proposals;
discarding any proposal which causes said production plan to
contradict said constraints;
computing the cost of implementing said production plan as modified
by each of said remaining proposals;
selecting a proposal which causes said production plan to have the
least computed cost;
repeating said above steps until no proposals remain after said
discarding step; and
providing the current production plan as a solution production
plan.
35. The method, as set forth in claim 34, wherein said constraint
formulating and applying steps comprise the steps of formulating
and applying a production capacity constraint of said manufacturing
facility to said theoretical plan, said manufacturing facility
having at least one machine and wherein said capacity constraint
formulating step further comprises the steps of:
storing and providing an availability of each machine;
controlling a work-in-process work load;
storing and providing a number of work hours of said manufacturing
facility; and
receiving said machine availability, work-in-process and work hours
and computing the maximum amount of usage of said machine.
36. The method, as set forth in claim 35, wherein said capacity
constraint formulating step comprises the steps of:
storing and providing an amount of usage per machine; and
receiving said machine usage and computing an amount of current
usage per machine in response thereto.
37. The method, as set forth in claim 36, said capacity constraint
formulating step further comprises the step of formulating said
production capacity of said manufacturing facility in response to
said maximum usage per machine and said current usage per
machine.
38. The method, as set forth in claim 34, wherein said constraint
formulating and applying steps comprise the steps of formulating
and applying a constraint describing the amount of surplus that is
feasibly produced by said manufacturing facility.
39. The method, as set forth in claim 38, said manufacturing
facility producing at least one type of product, and wherein said
surplus feasibility constraint formulating step further
comprises:
computing expected surplus per product type in response to said
theoretical production plan; and
formulating said surplus feasibility constraint in response to said
computed expected surplus.
40. The method, as set forth in claim 34 said manufacturing
facility manufactures in units of a fixed number and also in
partial units of a number less than said fixed number, wherein said
constraint formulating and applying steps comprise the steps of
formulating and applying a constraint describing the number of
partial production units that may be feasibly initiated by said
manufacturing facility.
41. The method, as set forth in claim 40, said partial unit
feasibility constraint formulating step comprises the steps of:
computing the number of units that are required in response to said
theoretical production plan;
computing the number of partial units that are required in response
to said theoretical production plan; and
formulating said partial unit feasibility constraint in response to
said computed number of units and partial units required for said
theoretical production plan.
42. The method, as set forth in claim 34, said manufacturing
facility producing at least one type of product, and wherein said
cost function computing step comprises the steps of:
computing an expected yield per product type;
receiving customer demand;
computing a push cost per product type in response to said computed
expected yield and said received customer demand;
computing a pull cost per product type in response to said computed
expected yield and said received customer demand; and
computing a cost function of said production plan in response to
said computed push and pull costs.
Description
TECHNICAL FIELD OF THE INVENTION
This invention relates in general to the field of scheduling
systems. More particularly, the present invention relates to
apparatus and a method for production planning.
BACKGROUND OF THE INVENTION
Production planning is the process of choosing work to be started
in a manufacturing facility during some future time period so that
performance is maximized. Work is usually selected from a variety
of product types which may require different resources and serve
different customers. Therefore, the selection must optimize
customer-independent performance measures such as cycle time and
customer-dependent performance measures such as on-time
delivery.
The reasons for requiring advanced production planning may be
unique to each manufacturing facility. For example, one facility
may require advanced planning so that materials may be ordered and
delivered in time for manufacture. Another facility may require
advanced planning in order to make delivery commitments or predict
delays in product delivery.
In order to configure a production plan which yields the best
performance, the capacity, or the amount of work the facility can
handle, must be modeled in some fashion, since starting work above
the capacity of the facility compromises performance and brings
forth no benefits. Conventional factory capacity models employ
simple steady-state linear relations that include: (1) the average
amount of available work time for each machine in the factory and
(2) the amount of work each product requires of each machine. From
the above linear relations, a given start plan is within capacity
if, for each machine, the total required amount of work is: (1)
less than the machine's available time, and (2) multiplied by a
predetermined fraction goal utilization of the start rate.
There are several problems associated with a linear production
planning program. Because of the large problem size, variables in
linear programs must be expressed in non-integer quantities in
order to yield good solutions. As a result, fractional start
quantities may be generated which must be converted into discrete
start quantities. Such forced conversion sacrifices the goodness of
the solution.
Additionally, non-linear relationships cannot be modeled in a
linear program. Examples of such relationships are the expected
yield for a product's start quantity, and the cost of surplus and
delinquency. Such non-linear relationships have been traditionally
coerced into linear expressions with loss of precision.
The large problem size presents another obstacle for linear
production planning programs. Even if a planning problem can be
expressed in a linear program, the problem size may prohibit
efficient solution via conventional linear programming techniques.
This problem has not been overcome in the industry without
substantial loss of optimality in the solution.
Therefore, a need has arisen for apparatus and method to formulate
a production plan for a manufacturing facility that accommodates
integer variables, allows non-linear expressions and provides a
near optimal production plan despite the large problem size.
SUMMARY OF THE INVENTION
In accordance with the present invention, apparatus and method for
production planning are provided which substantially eliminate or
reduce disadvantages and problems associated with prior production
planners.
In one aspect of the present invention, apparatus for production
planning in a manufacturing facility is provided. The apparatus
comprises means for generating a plurality of theoretical plans and
a constraint-based model for evaluating one of the theoretical
production plans, and applying at least one constraint thereto.
Further, a cost function is computed for each of the theoretical
production plans. Means is then provided for searching for a
feasible production plan among the plurality of theoretical plans
that does not violate any of the applied constraints and has the
least computed cost function value.
In another aspect of the present invention, apparatus for
production planning in a manufacturing facility is provided. The
apparatus comprises means for computing (e.g. computer) the
capacity of the factory in order to produce the determined
quantities and types of product, means for computing the maximum
factory capacity, and means for comparing the computed production
capacity with the maximum factory capacity. Further included are
means for computing the cost of producing the determined quantities
and types of product in response to the computed production
capacity being less than or equal to the maximum factory capacity
and means for selecting a production plan that has the least
computed cost function value.
In yet another aspect of the present invention, a method for
generating a production plan for a manufacturing facility is
provided, which comprises the steps of initializing the production
plan, and generating a plurality of proposals to modify the
production plan. At least one constraint is formulated and applied
to the production plan as modified by each of the plurality of
proposals. Any proposal which causes the production plan to
contradict the constraints is then discarded, after which the cost
of implementing the production plan as modified by each of the
remaining proposals is computed. A proposal which causes the
production plan to have the least computed cost is selected and the
above steps are repeated until no proposals remain after the
discarding step. The current production plan is then offered as the
solution production plan.
An important technical advantage of the present invention provides
a formulation of production planning as a cost minimization problem
using constraint-based models.
Another important technical advantage of the present invention
provides a production planner which employs a heuristic search
algorithm which iteratively manipulates a starting plan to reduce
the plan cost until no further manipulation improves the plan.
Yet another important technical advantage of the present invention
provides a more accurate production planner which accommodates real
variables and linear equalities as well as integer variables and
non-linear equalities.
BRIEF DESCRIPTION OF THE DRAWINGS
For a better understanding of the present invention, reference may
made to the accompanying drawings, in which:
FIG. 1 is a simplified block diagram showing the inputs and outputs
of the present invention;
FIG. 2 is a flowchart of a heuristic search algorithm in the
preferred embodiment of the present invention; and
FIG. 3 is a constraint flow diagram illustrating a planning model
in the preferred embodiment of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
With reference to the drawings, FIG. 1 illustrates some of the
input and output parameters of a preferred embodiment of the
apparatus and method for production planning for a manufacturing
facility, indicated generally at 10 and constructed according to
the teaching of the present invention. In order to formulate a
production plan 12, production planner 10 takes into consideration
inputs such as customer demand 14. Customer demand 14 may specify
the quantity and type of products ordered by the customer, and the
delivery date of the order. Customer demands 14 may also be
prioritized in the order of importance. The output or end product
of the manufacturing facility, when produced in accordance with
production plan 12, should preferably meet customer demand 14 and
yet not result in an over abundance in inventory. Similarly, there
is also penalty when customer demand 14 is not met by the
production plan 12. Therefore, associated with each production plan
12 is a plan cost 16, which represents the cost of implementing the
plan.
Another set of inputs 18 describes the constraints placed on
production planner 10 from facility related parameters, such as
machine capacity, down time, etc. Therefore, the production volume
is checked by facility constraints 18. Additional constraints 20
arising from the operation of the facility, such as yield, surplus
and work-in-process, also regulate the production quantity and type
of product that should be started.
Referring to FIG. 2, a flowchart 30 of a heuristic search algorithm
of the preferred embodiment of the present invention 10 (e.g. for a
general purpose computer) is shown. The present invention employs
the heuristic search algorithm to search for a suitable plan which
specifies the product type and quantity to be started at the
beginning of the next planning period without incurring high cost
or violating any facility or operational constraints 18 and 20. The
search algorithm starts by setting the quantities for all product
types to zero. For a semiconductor wafer fabrication facility, this
equates to setting the number of lots to be started to zero for all
device types. This results in the worst and highest cost plan,
since by producing nothing, none of the customer demands will be
met.
From the initial zero plan, a set of operators which proposes
changes to the plan is generated, as shown in block 34. The
operators may propose to modify the plan in two ways. They may
increase the number of lots to be started by one for a particular
device type, or they may set the number of lots to a determinable
number, so that critical customer orders for each device are
covered. All operators reachable from the current plan in the
above-identified ways are generated and examined to determine their
feasibility. Those operators which generate plans that contradict
facility or operational constraints are eliminated from the search,
as shown in block 36.
If there are remaining operators, as determined in decision block
38, then a plan cost is computed for each remaining proposed plan.
Of the remaining operators, the one which yields the most decrease
in computed plan cost per addition to work is selected, as shown in
block 44. The change in work may be defined as the change in the
amount of utilization of the current top bottleneck machine in the
current plan and may be computed by machine usage information 63.
The selected operator is then applied to the current plan, as shown
in block 46, to yield a new current plan. Execution then returns to
block 34 where another set of operators are generated from the new
current plan. The loop, including blocks 34 to 46, is repeated
until, at block 38, no operator remains which does not contradict
any constraints. The plan from which the last set of operators is
generated is the solution production plan that will yield low plan
cost, adds the least amount of work, and yet does not contradict
any constraints.
One may recognize the above-described search algorithm as a beam
search of width one, where each feasible plan constitutes a parent
node in the search tree, and the operators are the children nodes
of each parent node. The beam search algorithm of width one is used
in the preferred embodiment of the present invention because it
keeps the number of nodes searched to a manageable quantity in a
potentially sizeable search tree.
With reference to FIG. 3, the details of those factors which
contribute to the computation of plan cost, and facility and
operational constraints are shown. For ease of illustration, a
fictional semiconductor wafer fabrication facility which makes only
three types of devices and has only four machines will be used as
an example. Referring back to block 34 in FIG. 2, a set of
operators is generated which proposes to modify a current plan in
some fashion. The modifications proposed typically present a new
mix of product types and/or quantities. Therefore, a production
plan 50 may constitute variables 51-53, which represent the number
of lots to be started for each type of device.
In block 36 of the search algorithm shown in FIG. 2, the generated
operators must be examined to determine whether they violate
constraints imposed on variables 51-53. One is the constraint which
stems from facility capacity.
Each of variables 51-53, which represent the number of lots to be
started for each device, is operated upon by machine usage
constraints 55, which are derived from a capacity model 56 of each
machine in the facility. Such machine capacity modeling is known in
the art. The result is the amount of usage by each device type on
each piece of machinery 57. Note that since there are four
machines, there are four such variables 58-61. The amount of usage
per machine, per device, contributes partially to capacity
feasibility constraints 62. Therefore,
computes for the amount of usage required on each machine for the
plan, where LOT.sub.-- USAGE(MACHINE,PRODUCT) represents the amount
of usage required by each lot of each device on each machine, and
STARTS(PRODUCT) represents the number of lots to be started for
each product.
The maximum usage possible for each machine 63, which is computed
from a combination of factors such as machine availability due to
down time and setup time 64, work-in-process 65, and the number of
hours of operation 66 is used to compute the following:
where MAX.sub.-- FACTORY.sub.-- UTILIZATION specifies the goal
factory utilization, and MAX.sub.-- USAGE(MACHINE) is the maximum
usage per machine 63. Therefore, a plan is feasible with respect to
(MAX.sub.-- FACTORY.sub.-- UTILIZATION * MAX.sub.-- USAGE(MACHINE))
if STARTS(PRODUCT) values are such that, for every machine,
PLAN.sub.-- USAGE(MACHINE) utilizes the machines no greater than
the goal. The capacity constraints 62 further assure that if a
machine becomes a bottleneck in the production process, it is used
no more than the factory utilization goal. Typically, the factory
utilization goal is set by facility personnel.
The number of lots per device type is further regulated by expected
surplus constraints 68, which compute the expected surplus per
device 69 for the three device types 70-72. This relationship may
be expressed in the following fashion: ##EQU1## EXPECTED.sub.--
SURPLUS(PRODUCT) is the expected surplus for each product;
AVG.sub.-- OUTPUT(STARTS(PRODUCT)) equals to STARTS(PRODUCT) *
AVG.sub.-- YIELD(PRODUCT); TOTAL.sub.-- DEMAND(PRODUCT) is the
amount of all known demands for each product, including
non-startable demands; and MAX.sub.-- SURPLUS.sub.-- DEMAND.sub.--
RATIO is an input parameter predetermined by facility
personnel.
From the foregoing, it may be seen that surplus feasibility
constraint 73 states that if the lot-start number is positive for a
product, surplus is acceptable if the ratio of expected surplus to
total demand (computed from customer demand 74) does not exceed
MAX.sub.-- SURPLUS.sub.-- DEMAND.sub.-- RATIO.
A facility may choose to accommodate partial lots which contain a
fewer number of wafers than a full lot. Partial lots are useful to
meet small customer demands, but tend to utilize certain machines
poorly, such as batch machines like ovens. Therefore, in order to
ensure good facility utilization, a partial lot feasibility
constraint 75 is applied to the number of starting lots 50. From
the number of starting lots for each product 51-53, the number of
partial lots 76 and full lots 77 are computed by partial lot count
and full lot count constraints 78 and 79, respectively. Partial lot
feasibility constraint 75 may be expressed by the following:
##EQU2## where MAX.sub.-- PART.sub.-- LOT.sub.-- RATIO is an input
parameter determined by facility personnel.
Returning to block 36 in FIG. 2, it may be seen that the
above-described capacity, surplus feasibility, and partial lot
feasibility constraints are applied to the plan modification
proposed by each operator, and those operators which contradict the
constraints are removed from the search. It is important to note
that although specific constraints are shown herein, they merely
serve as examples of how constraints may be used in the present
invention to compute a production plan. Therefore, other
constraints known in the art may be applicable to the present
invention and are within the scope thereof.
In block 42, those remaining operators are applied to the current
plan to compute the cost of the modified plan. This computation is
shown in FIG. 3. The number of lots to be started for each product
type 51-53 are subject to a yield constraint to compute an expected
yield 81 for each device type 82-84. In the preferred embodiment of
the present invention, yield constraint 80 may be expressed by the
following statistical formula: ##EQU3## The average yield and
variance of each product, AVG.sub.-- YIELD(PRODUCT) and
VARIANCE(PRODUCT), are computed from previous yield values. If
desired, trend analysis and other methods to achieve better yield
prediction may also be used. K is an input parameter specifying a
measure of confidence in the chance that at least YIELD will be
produced from START for each product type. From the foregoing, it
may be recognized that higher K or confidence results in production
of sufficient quantity to more frequently meet customer demand.
However, more inventory may be produced, since more lots are
started per demand.
Expected yield for each device type 82-84 is subject to demand
constraints 85 and pull-ahead constraints 86 to compute push cost
and pull cost per device 87 and 88, respectively. Push cost 87 is
defined as the cost of not covering customer demand and pull cost
88 is defined as the cost of producing orders ahead of time.
Therefore, demand constraints 85 and pull-ahead constraints receive
input from customer demand 74. There are known formulas for
computing the push and pull costs, and will not be discussed
further herein.
The push cost per device 89-91 and pull cost per device 92-94 are
summed independently by summation constraints 95 and 96 to
calculate for the total push cost 97 and total pull cost 98 of the
plan. The total push and pull costs 97 and 98 are summed again by a
third summation constraint 99 to yield the total cost 100 of the
plan.
As mentioned above, the total plan cost 100 provides a measure of
the goodness of the plan. If an operator proposes a plan that costs
the least and adds the least amount of work among all remaining
operators and yields no feasible children operators in the search
tree, then the plan proposed by the operator is the solution
plan.
Although the present invention has been described in the
environment of a semiconductor wafer fabrication facility, the
constraint-based model combined with the heuristic search algorithm
as taught by the present invention is applicable to other
production environments. No particular form of hardware is required
for system operation. The preferred embodiment was designed with a
general computer in mind, but would work equally well with any
other computerized apparatus.
Furthermore, it should be understood that various changes,
substitutions and alterations can be made hereto without departing
from the spirit and scope of the present invention as defined by
the appended claims.
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